I am plotting trajectories in Matlab using contourf. I am having an issue with the colors matching the data. I have posted my current image below. All areas that do not have data should be white as they are zero which I specifically specified in the script(they are currently blue-ish which is the the 0.1 to 1 range). In addition, values that are yellow, should be in the blue range(<1). Any suggestions?
Here is the part of my script where I do the plotting:
axesm('mercator', 'MapLatLim', latlim, 'MapLonLim', lonlim,...
'Frame', 'on', 'Grid', 'on', 'MeridianLabel', 'on', 'ParallelLabel', 'on')
setm(gca,'mlabelparallel',-20)
load coastlines
Contours = [0.001 0.01 0.1 1 10 100];
[c,h] = contourfm(latlim, lonlim, u, log(Contours));
colorbar('YTick', log(Contours), 'YTickLabel', Contours);
myColorMap = jet(256).^.3;
myColorMap(1,:) = [1];
colormap(myColorMap)
colorbar
caxis(log([Contours(1) Contours(length(Contours))]));
colorbar('FontSize', 12, 'YTick', log(Contours), 'YTickLabel', Contours);
geoshow(coastlat, coastlon,'Color', 'k')
Contour level, V, in contourfm(lat,lon,Z, V) does not scale your data or colour. It works in a different way than what you thought.
Let's see one example first:
u = rand(8)+0.1; u(1:2,:) = 0; u(5:6,:) = 10; u(7:8,:) = 100;
V = [0,1,40,100];
contourfm([0,1], [0,1], u, V);
mycm = jet(256).^.3; mycm(1,:) = 1;
colormap(mycm)
contourcbar('FontSize', 12, 'YTick', V, 'YTickLabel', V);
where u is
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
0.1947 0.6616 0.2413 0.6511 0.4403 0.9112 1.0016 0.5654
0.8422 0.3159 0.5695 0.6478 0.9933 0.1686 0.8387 0.5362
10 10 10 10 10 10 10 10
10 10 10 10 10 10 10 10
100 100 100 100 100 100 100 100
100 100 100 100 100 100 100 100
As you can see, for V = [0,1,40,100] all values from 0 to 1 are white, values from 1 to 40 are cyan and above are red.
Therefore, you must scale your u then assign appropriate contour level. Use contourcbar instead of colorbar to check the colours first.
Apart from the problem with contour level, I suspect the u parameter contains negative values. The colour at the bottom of the colour bar is always assigned to the minimum z value. You must ensure 0 is the minimum value in u, i.e. remove the negative values.
Related
I've written some code in MATLAB that converts an image (of stars) into a grayscale image and then into a binary image using a set threshold and then labels each cluster of pixels (stars) that is above this threshold. The labelling produces an output:
e.g.
[1 1 1 0 0 0 0 0 0
1 1 0 0 0 2 2 2 0
0 0 0 3 3 0 2 0 0
0 0 0 3 3 0 0 0 0]
So each cluster of 1's, 2's, 3's etc. represents a star. After this the code then finds the centroids of each pixel cluster and draws a bounding box around each centroid (centered on the centroid) with an 8 x 8 pixel area. The bounding box limits are made by finding xmax, xmin, ymax, ymin of each calculated centroid, which involves either adding or subtracting 4 (pixels) from the x and y coordinates of each centroid.
The weighted centroid is calculated like so:
x_coordinate_centroid = sum(x_coordinate .* pixel_values) / sum_pixel_values
y_coordinate_centroid = sum(y_coordinate .* pixel_values) / sum_pixel_values
x/y_coordinate and pixel values are for the pixels contained within each bounding box.
The bounding box would surround an 8 x 8 pixel area (with the given intensities) on the grayscale image such as:
[100 100 100 90 20 20 0 0
80 90 100 90 20 30 0 0
50 70 100 70 30 0 20 0
50 0 0 60 30 30 0 0
0 0 0 0 0 0 0 0
0 50 0 0 0 0 0 0
0 40 0 0 0 0 0 0
0 20 0 0 0 0 0 0]
The top left value ([xmin, ymax]), for example, could have image coordinates [41, 14] and an intensity of 100.
The output from my code, for example, could give 5 bounding boxes across the grayscale image. I now need to write code that automatically calculates the weighted centroid of each bounding box region. I'm not sure how to go about this, does anyone have any ideas how this can be achieved?
My code for calculating the centroids and their bounding boxes is shown below.
%% Calculate centroids of each labelled pixel cluster within binary image
N = max(B(:)); % total number of pixel labels generated in output array
sum_total = zeros(N,1); % create N x 1 array of 0's
sum_yv = zeros(N,1); % "
sum_xv = zeros(N,1); % "
for xx=1:size(B,2) % search through y positions
for yy=1:size(B,1) % search through x positions
index = B(yy,xx);
if index>0
sum_total(index) = sum_total(index) + 1;
sum_yv(index) = sum_yv(index) + yy;
sum_xv(index) = sum_xv(index) + xx;
end
end
end
centroids = [sum_xv, sum_yv] ./ sum_total; % calculates centroids for each cluster
x_lower_limits = centroids(:,1)-4;
y_lower_limits = centroids(:,2)+4; % lower on image means larger y coord number
x_upper_limits = centroids(:,1)+4;
y_upper_limits = centroids(:,2)-4; % higher on image means lower y coord number
x_lower_limits(x_lower_limits<1)=1; % limit smallest x coord to image axis (1,y)
y_lower_limits(y_lower_limits>size(binary_image,1))=size(binary_image,1); % limit largest y coord to image axis (x,517)
x_upper_limits(x_upper_limits>size(binary_image,2))=size(binary_image,2); % limit largest x coord to image axis (508,y)
y_upper_limits(y_upper_limits<1)=1; % limit smallest y coord to image axis (x,1)
width = x_upper_limits(:,1) - x_lower_limits(:,1); % width of bounding box
height = y_lower_limits(:,1) - y_upper_limits(:,1); % height of bounding box
hold on
for xl=1:size(x_lower_limits,1)
r(xl)=rectangle('Position',[x_lower_limits(xl,1) y_upper_limits(xl,1) width(xl,1) height(xl,1)],'EdgeColor','r');
end
for i=1:size(centroids,1)
plot(centroids(i,1),centroids(i,2),'rx','MarkerSize',10)
end
hold off
%%
For example, using the following code, I have a coordinate matrix with 3 cubical objects defined by 8 corners each, for a total of 24 coordinates. I apply a rotation to my coordinates, then delete the y coordinate to obtain a projection in the x-z plane. How do I calculate the area of these cubes in the x-z plane, ignoring gaps and accounting for overlap? I have tried using polyarea, but this doesn't seem to work.
clear all
clc
A=[-100 -40 50
-100 -40 0
-120 -40 50
-120 -40 0
-100 5 0
-100 5 50
-120 5 50
-120 5 0
-100 0 52
-100 0 52
20 0 5
20 0 5
-100 50 5
-100 50 5
20 50 52
20 50 52
-30 70 53
-30 70 0
5 70 0
5 70 53
-30 120 53
-30 120 0
5 120 53
5 120 0]; %3 Buildings Coordinate Matrix
theta=60; %Angle
rota = [cosd(theta) -sind(theta) 0; sind(theta) cosd(theta) 0; 0 0 1]; %Rotation matrix
R=A*rota; %rotates the matrix
R(:,2)=[];%deletes the y column
The first step will be to use convhull (as yar suggests) to get an outline of each projected polygonal region. It should be noted that a convex hull is appropriate to use here since you are dealing with cuboids, which are convex objects. I think you have an error in the coordinates for your second cuboid (located in A(9:16, :)), so I modified your code to the following:
A = [-100 -40 50
-100 -40 0
-120 -40 50
-120 -40 0
-100 5 0
-100 5 50
-120 5 50
-120 5 0
-100 0 52
-100 0 5
20 0 52
20 0 5
-100 50 5
-100 50 52
20 50 5
20 50 52
-30 70 53
-30 70 0
5 70 0
5 70 53
-30 120 53
-30 120 0
5 120 53
5 120 0];
theta = 60;
rota = [cosd(theta) -sind(theta) 0; sind(theta) cosd(theta) 0; 0 0 1];
R = A*rota;
And you can generate the polygonal outlines and visualize them like so:
nPerPoly = 8;
nPoly = size(R, 1)/nPerPoly;
xPoly = mat2cell(R(:, 1), nPerPoly.*ones(1, nPoly));
zPoly = mat2cell(R(:, 3), nPerPoly.*ones(1, nPoly));
C = cell(1, nPoly);
for iPoly = 1:nPoly
P = convhull(xPoly{iPoly}, zPoly{iPoly});
xPoly{iPoly} = xPoly{iPoly}(P);
zPoly{iPoly} = zPoly{iPoly}(P);
C{iPoly} = P([1:end-1; 2:end].')+nPerPoly.*(iPoly-1); % Constrained edges, needed later
end
figure();
colorOrder = get(gca, 'ColorOrder');
nColors = size(colorOrder, 1);
for iPoly = 1:nPoly
faceColor = colorOrder(rem(iPoly-1, nColors)+1, :);
patch(xPoly{iPoly}, zPoly{iPoly}, faceColor, 'EdgeColor', faceColor, 'FaceAlpha', 0.6);
hold on;
end
axis equal;
axis off;
And here's the plot:
If you wanted to calculate the area of each polygonal projection and add them up it would be very easy: just change the above loop to capture and sum the second output from the calls to convexhull:
totalArea = 0;
for iPoly = 1:nPoly
[~, cuboidArea] = convhull(xPoly{iPoly}, zPoly{iPoly});
totalArea = totalArea+cuboidArea;
end
However, if you want the area of the union of the polygons, you have to account for the overlap. You have a few alternatives. If you have the Mapping Toolbox then you could use the function polybool to get the outline, then use polyarea to compute its area. There are also utilities you can find on the MathWorks File Exchange (such as this and this). I'll show you another alternative here that uses delaunayTriangulation. First we can take the edge constraints C created above to use when creating a triangulation of the projected points:
oldState = warning('off', 'all');
DT = delaunayTriangulation(R(:, [1 3]), vertcat(C{:}));
warning(oldState);
This will automatically create new vertices where the constrained edges intersect. Unfortunately, it will also perform the triangulation on the convex hull of all the points, filling in spots that we don't want filled. Here's what the triangulation looks like:
figure();
triplot(DT, 'Color', 'k');
axis equal;
axis off;
We now have to identify the extra triangles we don't want and remove them. We can do this by finding the centroids of each triangle and using inpolygon to test if they are outside all 3 of our individual cuboid projections. We can then compute the areas of the remaining triangles and sum them up using polyarea, giving us the total area of the projection:
dtFaces = DT.ConnectivityList;
dtVertices = DT.Points;
meanX = mean(reshape(dtVertices(dtFaces, 1), size(dtFaces)), 2);
meanZ = mean(reshape(dtVertices(dtFaces, 2), size(dtFaces)), 2);
index = inpolygon(meanX, meanZ, xPoly{1}, zPoly{1});
for iPoly = 2:nPoly
index = index | inpolygon(meanX, meanZ, xPoly{iPoly}, zPoly{iPoly});
end
dtFaces = dtFaces(index, :);
xUnion = reshape(dtVertices(dtFaces, 1), size(dtFaces)).';
yUnion = reshape(dtVertices(dtFaces, 2), size(dtFaces)).';
totalArea = sum(polyarea(xUnion, yUnion));
And the total area for this example is:
totalArea =
9.970392341143055e+03
NOTE: The above code has been generalized for an arbitrary number of cuboids.
polyarea is the right way to go, but you need to call it on the convex hull of each projection. If not, you will have points in the centers of your projections and the result is not a "simple" polygon.
I have two vectors as follows:
x = 0:5:50;
sir_dB = [50 20 10 5 2 0 -5 -10 -20 -20 -20]
Where x denotes the distance on the x-axis and sir_dB the SNR. For this, I need to generate a color map for a grid of 50 x 60m something similar to this:
based on the value of sir_dB.
I tried the following:
sir_dB = [50 20 10 5 2 0 -5 -10 -20 -20 -20];
xrange = 0:50;
yrange = -30:30;
% create candidate set
[X, Y] = ndgrid(xrange, yrange); % grid of points with a spacing of 1.
candidate_set = [X(:), Y(:)];
test_pt = [0 30];
radius = 5;
% find which of these are within the radius of selected point:
idx = rangesearch(candidate_set, test_pt, radius );
neighborhood = candidate_set(idx{1}, :);
Once I have the neighbors at a radius of 5m, I need to color that part of the grid based on the sir_dB value for a corresponding x value.
I need to have the plot in such a way that for all values of sir_dB greater than 15, the grid should be colored green, yellow for y greater than 0 and red for y greater than -20.
Could someone provide me inputs of how to do this best?
Im not sure exactly what you want, but this should get you started with contourf. I increased the granularity of xrange and yrange to make the radius more smooth but you can change it back if you want.
x = 0:5:50;
sir_dB = [50 20 10 5 2 0 -5 -10 -20 -20 -20];
xrange = 0:0.1:50;
yrange = -30:0.1:30;
% create candidate set
[X, Y] = ndgrid(xrange, yrange); % grid of points with a spacing of 1.
candidate_set = [X(:), Y(:)];
test_pt = [0 30];
r = sqrt((test_pt(1)-X(:)).^2 + (test_pt(2)-Y(:)).^2);
idx = r>5;
snr = nan(size(X));
snr(idx) = interp1(x,sir_dB,X(idx),'linear');
% Some red, yellow, green colors
cmap = [0.8500 0.3250 0.0980;
0.9290 0.6940 0.1250;
0 0.7470 0.1245];
figure();
colormap(cmap);
contourf(X,Y,snr,[-20,0,15],'LineStyle','none');
Plotting the the contour plot alongside the original sir_dB we see that it lines up (assuming you want linear interpolation). If you don't want linear interpolation use 'prev' or 'next' for the interp1 method.
figure();
colormap(cmap);
subplot(2,1,1);
contourf(X,Y,snr,[-20,0,15],'LineStyle','none');
subplot(2,1,2);
plot([0,50],[-20,-20],'-r',[0,50],[0,0],'-y',[0,50],[15,15],'-g',x,sir_dB);
Here is another suggestion, to use imagesc for that. I nothed the changes in the code below with % ->:
x = 0:5:50;
sir_dB = [50 20 10 5 2 0 -5 -10 -20 -20 -20];
xrange = 0:50;
yrange = -30:30;
% create candidate set
[X, Y] = ndgrid(xrange, yrange); % grid of points with a spacing of 1.
% -> create a map for plotting
Signal_map = nan(size(Y));
candidate_set = [X(:), Y(:)];
test_pt = [10 20];
radius = 35;
% find which of these are within the radius of selected point:
idx = rangesearch(candidate_set,test_pt,radius);
neighborhood = candidate_set(idx{1}, :);
% -> calculate the distance form the test point:
D = pdist2(test_pt,neighborhood);
% -> convert the values to SNR color:
x_level = sum(x<D.',2);
x_level(x_level==0)=1;
ColorCode = sir_dB(x_level);
% -> apply the values to the map:
Signal_map(idx{1}) = ColorCode;
% -> plot the map:
imagesc(xrange,yrange,rot90(Signal_map,2))
axis xy
% -> apply custom color map for g-y-r:
cmap = [1 1 1 % white
1 0 0 % red
1 1 0 % yellow
0 1 0];% green
colormap(repelem(cmap,[1 20 15 35],1))
c = colorbar;
% -> scale the colorbar axis:
caxis([-21 50]);
c.Limits = [-20 50];
c.Label.String = 'SNR';
The result:
I'm plotting z values, 0 to 10, on a contour plot.
When I include data 1 or greater, I obtain a contour plot. Like the following:
longitude = [80 82 95]
latitude = [30 32 35]
temp = [1 4 6; 1 2 7; 3 5 7]
contourf(longitude,latitude,temp)
Now, I want to plot the ZERO VALUE also on the contour plot. While I was expecting one color representing the zero value, instead I obtained a white square.
longitude = [80 82 95]
latitude = [30 32 35]
temp = [0 0 0; 0 0 0; 0 0 0]
contourf(longitude,latitude,temp)
Thanks a lot,
Amanda
As Issac mentioned. To plot a constant data in a contourf is not possible.
When you try to do so you will obtain this warning from Matlab:
temp =
0 0 0
0 0 0
0 0 0
Warning: Contour not rendered for constant ZData
> In contourf>parseargs at 458
In contourf at 63
In TESTrandom at 45
However, if you put some numbers as 0, the contourf works fine:
longitude = [80 82 95];
latitude = [30 32 35];
temp = [0 4 6; 1 0 7; 0 5 9];
contourf(longitude,latitude,temp);
hcb = colorbar('horiz'); % colour bar
set(get(hcb,'Xlabel'),'String','Contourf Bar.')
I have a 2D binary matrix that I want to display as a black and white plot. For example, let's say I have a 4-by-4 matrix as follows:
1 1 0 1
0 0 1 0
1 1 0 1
1 0 0 0
How can this be plotted as a black and white matrix? Some of my input binary matrices are of size 100-by-9, so I would ideally need a solution that generalizes to different sized matrices.
If you want to make a crossword-type plot as shown here (with grid lines and black and white squares) you can use the imagesc function, a gray colormap, and modify the axes properties like so:
mat = [1 1 0 1; 0 0 1 0; 1 1 0 1; 1 0 0 0]; % Your sample matrix
[r, c] = size(mat); % Get the matrix size
imagesc((1:c)+0.5, (1:r)+0.5, mat); % Plot the image
colormap(gray); % Use a gray colormap
axis equal % Make axes grid sizes equal
set(gca, 'XTick', 1:(c+1), 'YTick', 1:(r+1), ... % Change some axes properties
'XLim', [1 c+1], 'YLim', [1 r+1], ...
'GridLineStyle', '-', 'XGrid', 'on', 'YGrid', 'on');
And here's the image you should get:
I'm not sure if I got your question right, but you may try the image function, like this:
A = [ 1 1 0; 1 0 1; 1 1 1 ];
colormap([0 0 0; 1 1 1 ]);
image(A .* 255);
Try the spy function to start with perhaps.